Proceeding of The 6 Mathematics Conference of Payame Noor University

توضیحات

ABSTRACT

Bornological and b-bornological locally convex cones have been studied in [D. Ayaseh and A. Ranjbari, Bornological
Locally Convex Cones, Le Matematiche, 69(2)(2014), 267-284]. In this paper, we show that the projective limit of bornologi-cal cones is not bornological in general by an example. Also, we present an example of a nonbornological locally convex cone.

INTRODUCTION

A cone is a set P endowed with an addition and a scalar multiplication for nonnegative real numbers. The addition is assumed to be associative and commutative, and there is a neutral element 0 2 P. For the scalar multiplication the usual associative and distributive  properties hold, that is a(b a) = (ab )a, (a +b )a =aa+b a, a(a+b) =aa+ab, 1a = a and 0a = 0 for all a;b 2P and a;b  0. The theory of locally convex cones as developed in [3] and [8] uses an order theoretical concept or convex quasiuniform structure to introduce a topological structure on a cone. In this paper we use the latter. LetP be a cone. A collection U of convex subsetsU P2 =PP is called a convex quasiuniform structure onP, if the following
properties hold
(U1) Δ U for every U 2 U (Δ = f(a;a) : a 2Pg)
(U2) For all U;V 2 U there is aW 2 U such thatW U \V
(U3) lUomU  (l +m)U for all U 2 U and l ;m > 0
(U4) aU 2 U for all U 2 U and a > 0

 Year : 2015

Publisher : Payame Noor University

By : Farshad Mahdifar

File Information : English Language /83 Page / Size : 2.4 M

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سال : 2015

ناشر : دانشگاه پیام نور

کاری از : فرشاد مهدی فر

اطلاعات فایل : زبان انگلیسی /83 صفحه /حجم : 2.4 M

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